Re: What's "Developmentally Appropriate"?

[Bernard Cleyet <anngeorg@PACBELL.NET>]

Check out the little book;  "Calculus By and For Young People"  Don
Cohen [ISBN #0-9621674-1-X]

for example:

http://www.shout.net/~mathman/ <http://www.shout.net/%7Emathman/>


I supply the info., you decide.

bc



Jack Uretsky wrote:

> Brian, I bet that was easy for you to say.  But small change of a variable
> goes along with small change of a "matched variable" (whatever that might
> mean to a six-year old) is not a law of nature, it is a property of a
> highly restricted class of functions.  And in a "named ratio"?  It's hard
> to teach "ratio" to college students.  Six-year olds are grasping addition
> and subtraction of pairs of numbers in usual schools.  Do they really have
> the frontal lobes (or whatever the late developing part of the brain is)
> needed to deal with these concepts.
>
>        I think that a detailed explanation of Ms. Nishijima's definition
> of "success" would be most illuminating.  I don't pooh-pooh it, I simply
> don't understand it.
>
> On Sat, 11 Oct 2003, Brian Whatcott wrote:
>
>
>
> > At 12:49 PM 10/11/2003 -0500, Jack, you wrote
> >
> >
> >
> > > On Fri, 10 Oct 2003, Richard Hake wrote:
> > >
> > >
> > > Alan Kay wrote (quoted by permission...):
> > >
> > >
> > > > I have observed a very
> > > > talented 1st grade teacher - Julia Nishijima - teach the deep ideas
> > > > of the differential and integral calculus to her 6 year olds with
> > > > 100% success.
> > >        Wow!  Does anyone know what "success" means in this context?
> > >
> > >                        Regards,
> > >                                Jack
> > I speculate that "success" in teaching deep ideas of calculus by additive
> > examples, means that a six year old would be able to
> > identify a situation where a small increase in one variable
> > is associated with a small change in a matched variable
> > in a named ratio, and that the sum of the values of a matched variable
> > can be counted between boundaries specified in a given variable that
> > is associated with the counted variable.
> >
> >
> >
> > Brian Whatcott    Altus OK    Eureka!
>
> --
> "Don't push the river, it flows by itself"
>                                Frederick Perls